I was having the exact same problem — all of my pixel brushes disappeared in Designer v2, including the basic ones that come with the app.
The solution here worked for me — uninstall all v1 and v2 apps, then reinstall v2 apps, which will require reactivating. I hope there’s a better solution soon because I spent hours of time backing up hundreds of illustrations, and I wasn’t quite ready to start using v2 exclusively. I’m definitely going to do a better job of backing up as I go from now on, and closing designs I’ve completed.
If it helps, I think the issue started after I installed a bunch of True Grit Texture Supply Beat Tones brushes and some RetroSupply brushes to Designer 2.